Greatest Common Factor of 45 and 65 by Prime Factorization

Given Numbers: 45, 65
Identify the Prime Factors of 45 and 65 by Prime Factorization

• Prime Factorization of 45: 45 = 3 x 3 x 5 = 3² x 5¹
• Prime Factorization of 65: 65 = 5 x 13 = 5¹ x 13¹

Determine the Prime Factor(s) that are common to the Prime Factorization of each number:

• 5 is the only Prime Factor common to the Prime Factorizations of 45 and 65

Determine the least number of occurrences of 5 among the Prime Factorizations:

• 5 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 45 and 65 is equal to 5, which equals 5 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF (45, 65) = 5¹
• GCF(45, 65) = 5

Therefore, the Greatest Common Factor of 45 and 65 by Prime Factorization = 5